Decentralized Energy Management Platform

ABSTRACT

A method for power management includes applying a decentralized control to manage a large-scale community-level energy system; obtaining a global optimal solution satisfying constraints between the agents representing the energy system&#39;s devices as a state-based potential game with a multi-agent framework; independently optimizing each agent&#39;s output power while considering operational constraints and assuring a pure Nash equilibrium (NE), wherein a state space helps coordinating the agents&#39; behavior in energy system to deal with system-wide constraints including supply demand balance, battery charging power constraint and satisfy system-wide and device-level (local) operational constraints; and controlling distributed generations (DGs) and storage devices using the agent&#39;s output.

This application claims priority to application Ser. Nos. 61/978,065 and62/055,422, the contents of which are incorporated by reference.

BACKGROUND

The present invention relates to a decentralized management platform.

One goal of an energy management system (EMS) in power networks is tobalance the supply and demand in a cost efficient manner given itsoperating horizon, and uncertainties in generation due to renewablegenerators and in demand. There are centralized approaches available inthe literature to solve this problem. However, they are not scalable. Toadd any new device into the energy system, the centralized managementsystems need to be interrupted, updated and remodeled for any specificnew change in the system model. Moreover, as to reliability, anymalfunction of the central controller andor any device results candisrupt the operation of the whole system. There are also somedistributed management methods which mostly employ heuristic algorithms.However, these approaches cannot analytically guarantee the optimalityof the solution, reliability, and scalability of the system.

Moreover, management of energy systems in community level includingdistributed generations (DGs) and storage devices can be challenging dueto intermittent and uncontrollable nature of many types of DGs, energysources with different rates, and the following issues:

-   -   1. Scalability: The community-level energy systems are large in        size, and are also capable to grow more and add new components        during their lifetime. Adding any new device introduces new set        of parameters, objectives, and constraints in the operation of        these systems. As a result, the management platform should be        able to integrate the new devices without any interruption for        updating its control algorithm.    -   2. Reliability: The malfunction of any device in the system        should not result in an interrupt in the operation of the whole        system. According to DOE reliability requirements, management        systems should guarantee at least 98% reliability to supply        critical loads without any outage times.    -   3. Efficiency: Due to large size of the management problem for        these systems, achieving long-term optimal total cost and        real-time operation of energy systems is another challenge for        management systems.

SUMMARY

In one aspect, a method for decentralized energy management includescollecting information on neighboring power generators; solving adecentralized economic dispatch problem (D-EDP) and incorporating theD-EDP into a receding horizon control; generating a schedule for thepower generators based on a forecast of renewable generations and powerload; and updating the forecasts locally, where a forecast of renewablegeneration only needs to be known by the renewable generator deviceitself and a load device is introduced as a separate device thatcommunicates the forecasted demand to all the other units.

In another aspect, a method for power management includes applying adecentralized control to manage a large-scale community-level energysystem; obtaining a global optimal solution satisfying constraintsbetween the agents representing the energy system's devices as astate-based potential game with a multi-agent framework; independentlyoptimizing each agent's output power while considering operationalconstraints and assuring a pure Nash equilibrium (NE), wherein a statespace helps coordinating the agents' behavior in energy system to dealwith system-wide constraints including supply demand balance, batterycharging power constraint and satisfy system-wide and device-level(local) operational constraints; and controlling distributed generations(DGs) and storage devices using the agent's output.

In another aspect, a decentralized management platform based onmultiagent framework and state-based potential game is disclosed. Incontrast to most of the current heuristic control methods for multiagentenergy systems, this approach analytically obtains the global optimalsolution satisfying constraints between the agents (energy system'sdevices). The potential game is used to design the power managementproblem as a game. In this way, each agent is able to independentlyoptimize its output power while considers its operational constraints.More important, designed game assures that the pure Nash equilibrium(NE) exists. Moreover, an extension form of potential games, state-basedpotential game, is employed. The state space added to the game will helpwith coordinating the agents' behavior in energy system to deal withsystem-wide constraints such as supply demand balance, battery chargingpower constraint, etc. As a result, the NE of the game will not only beefficient with respect to system total cost of operation, but alsosatisfy all system-wide and device-level (local) operationalconstraints.

In another aspect, a decentralized management platform includes amulti-agent framework and a decentralized control method to manage thelarge-scale community-level energy systems. The Multi-agent frameworkfor energy systems includes a procedural architecture to add devices asagents into the energy system framework and submit the services theyprovide for or request from other agents. This framework is dynamic inwhich agents can join or leave the energy system at any time withoutinterrupting the rest of the system. Supplier agent includes deviceswhich can provide power to supply the load submit their service as asupplier and play as an active agent in the multi-agent framework. Theexample of these agents can be grid, diesel, PV, battery, etc. It shouldbe noted that battery can be both supplier agent and demand agent.Demand agents includes loads in the network will submit their service asdemand in multi-agent framework and inform supplier agents about theirrequested load value.

In another embodiment, a decentralized power management method includesa distributed dispatching strategy for energy sources and loads based ona special class of game theory, state-based potential game, and alearning algorithm such as gradient play or Newton method. This strategynot only minimizes the total marginal cost of operation for the wholeenergy system but also satisfies both device-level and system-wide leveloperational constraints.

Implementations include system-wide & local energy cost model: The totalcost of operation for the energy system (system-wide cost model) is thesummation of the devices' operational cost (local cost models).System-wide & local operational constraint can be used. Agents' localconstraints such as diesel generator capacity are handled locally by therelated agent. In order to achieve the minimum system-wide operationalcost in a distributed manner, agents use learning algorithms (gradientplay or Newton method) at each iteration of the game.

Advantages of the above aspects may include one or more of thefollowing. The system provides an efficient, scalable and reliablesolution. Regarding the scalability, each device is self-operated inthis platform and the energy system works in a plug-and-play manner.Hence, adding any new device will not interrupt system operation and notrequire updating the system modeling and consequently the controlalgorithm.

Furthermore, the reliability and robustness of the system operation willbe assured in this platform since the central controller will be removedfrom the system. Also, any malfunction of devices or communicationnetwork will only affect the related section and does not interrupt thewhole system operation. Last but not least, the proposed method isefficient and guarantees obtaining the minimum operational cost ofoperation.

The system provides a reliable and scalable decentralized platform thatefficiently manages the operation of a large-scale energy system basedon requested load, available renewable generation, time-of-use gridelectricity rate, battery condition, diesel generator loading-basedcost, etc. In this dynamic platform, any device can join or leave theenergy system at any time without interrupting the rest of the system.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A-1D show an exemplary d-EMS process.

FIG. 2 shows an exemplary system running the process of FIGS. 1A-1C.

DESCRIPTION

An EMS controls all the devices in a power network with the goal of costeffective performance while matching demand at all times. This goal istranslated as the economic dispatch problem (EDP). A centralizedmanagement system that solves the EDP requires information from alldevices, is prone to catastrophic failures. In addition, centralized EMShas scalability issue for any future expansion. The EMS is interruptedfor the integration of any new device to incorporate its operation costand device specific constraints to the algorithm that EMS implements.Similarly, when a device is up for maintenance a complete shutdown isrequired. That is, any failure in the EMS or a device in the networkenforces a system-wide operation interruption. These issues are overcomewith a decentralized energy management system.

To solve scalability issues due to introduction of new generator orstorage units and in robustness due to failures in some of the entitiesin the grid including the EMS itself in a centralized energy managementsystem, a decentralized energy management system (d-EMS) is developed.The d-EMS embeds a decentralized solution to the economic dispatchproblem (EDP) based on the alternating direction method of multipliers(ADMM) inside a decentralized implementation of the receding horizoncontrol. The ADMM based algorithm solves the EDP for the schedulinghorizon. The receding horizon control allows the system to adapt tochanges in the forecasts and network configuration. Decentralizedprotocols to handle changes to the communication network of devices isprovided. These device failure and addition protocols entail networkinformation updates only, thanks to the simple initialization of theADMM algorithm.

Our decentralized solution to the economic dispatch problem (d-EDP) isshown in FIGS. 1A-1D, which is an ADMM algorithm that operates on thedual of the EDP. The d-EDP derivation entails reformulating the dual ofthe EDP as a consensus problem on the price of power imbalance, that is,each device keeps a local price for power imbalance but is constrainedto agree with its neighbors on the local price. This reformulationadmits a decentralized solution using the ADMM algorithm. In the d-EDP,each device synchronously updates individual power and storage profilevariables as well as the local price variable by solving a min-maxproblem. Then devices exchange their local prices with their neighborsand do an ascent step on the dual variables of the local consensusconstraints. The algorithm converges to the optimal solutionasymptotically when the original problem has strong duality and isconvex, and the network is connected. We argue that the asymptoticoptimality result carries over to the EDP when the network is connectedand cost of each device is convex. Numerical implementations show thatconvergence to the optimal solution is fast and furthermore a nearfeasible solution is reached early. Here we explore the effects ofcommunication network topology and show that the convergence can degradewith the diameter of the network.

The EMS faces uncertainty in supply due to renewables and in demand. Asa result the EDP is solved based on predictions of renewables and demandinto the time horizon. As time progresses EMS can correct itspredictions and make new predictions for the new horizon based on newinformation revealed. To this purpose, we consider a receding horizoncontrol which makes up for prediction errors by solving the EDP for thewhole horizon, applying the first time step of the scheduled optimalactions and then solving the EDP at the next stage based on updatedforecasts. We present a communication protocol that allows for adecentralized implementation of the receding horizon control. The d-EDPcoupled with the receding horizon control amounts to a fullydecentralized EMS (d-EMS). Finally, we consider scalability androbustness. We show that the d-EMS can incorporate new devices thatregister and handle device failures on the fly via a simple update ofnetwork information during receding horizon control algorithm execution.

Referring now to FIGS. 1A-1C, an exemplary Decentralized EnergyManagement System (d-EMS) process according to our invention isdetailed. First, the system registers with a notification module andinitializes time to zero and the optimization horizon. A neighbor listis created. The system also obtains the devices and sets flags.

Next, the process checks if the device fail flag has been set and if sojumps to connector 1 (FIG. 1C) and otherwise performs the d-EDPoptimization and local updates are performed (FIG. 1B). Next, theprocess implements first element of power and storage schedule andincrements time and recedes the optimization horizon. The processinforms the neighbors of the time and receives time from the neighbors.Next, the process checks if all neighbors in a list has sent time and ifso jumps to connector 2 and otherwise checks if the device fail flag hasbeen set. If not, the process continues to receive time from neighborsand otherwise jumps to connector 1.

Continuing from FIG. 1A, FIG. 1B shows in more details the decentralizedeconomic dispatch algorithm. In this process, the iteration counter iscleared and each device sends price to neighbors and also observesprices from all neighbors. Each device then checks if the fail flag hasbeen set and if so, jumps to connector 1 and otherwise updates thevariables using price observations. Each device also updates prices andpower and storage schedules. Next, it checks if the max counter has beenreached and if so the process saves power and storage schedule andcontinues to the receding horizon control of FIG. 1A. Otherwise theprocess increments the iteration counter and then checks for devicefailure. If the device fail flag is set, then the process jumps toconnector 1 and otherwise jumps to connector 5.

FIG. 1C shows the Online Decentralized Device Reconfiguration. Fromconnector 1, the process updates network information including thenumber of neighbors, agents and clears the device fail flag and jumps toconnector 3. Alternatively, from connector 2, the process checks if thenew device flag is set and if so clears the new device flag and jumps toconnector 1. Otherwise, before jumping to connector 4, each devicereconfigures itself:

-   -   Update its forecasts of generation & storage capacity    -   Receive demand forecasts from Load agent    -   Initialize primal variables (power and storage schedules and        prices)    -   Set dual variables to zero

Turning now to FIG. 1D, the Online Decentralized Device ReconfigurationNotification Module, is disclosed. The process checks if a device failsor registers and if not, loops back to continue checking. Otherwise, ifthe number of devices have decreased the device failure notification(Device Fail flag=1) is sent to registered devices and otherwise a newdevice notification (New Device flag=1) is sent to registered devices.

In energy systems, EDP considers cost optimal power dispatch decisionsto match the load profile. We use d (h) to denote the predicted demandat time h∈H and the demand profile is defined as d:=[d(1), . . . ,d(H)]. We assume that the load profile d is known or d represents thepredicted load profile. The energy system is composed of devices N thatcan generate, store or generate and store power. We use G and S todenote the set of generator and storage units, respectively. The set ofall devices in the system is then the union of generator and storageunits, N:=G∪S.

A generator unit i∈G has the ability to inject p_(i)(h)≧0 amounts ofpower to the system at time h∈H not to exceed its generation capacityp_(i) ^(max)(h). The generation profile p_(i):={p_(i)(h)}_(h∈H) resultsin monetary cost of C_(i)(p_(i)) for the system where C_(i)(p_(i)) issome increasing function that maps load profile to positive reals R⁺.

A storage unit i∈G can chargedischarge its battery by s_(i)(h) amountsof power not to exceed its maximum chargedischarge amount s_(i)^(max)(h). When s_(i)(h)>0, we say that the storage unit charges itsbattery otherwise we say that it discharges its battery. The battery'sstate of charge at time h∈H is denoted by q_(i)(h)≧0 and is modeled bythe following difference equation,

q _(i)(h)=q _(i)(h−1)+αs _(i)(h)  (1)

where α is the coefficient converting kW units into Ah (includes timeinterval). The state of charge cannot exceed q_(i) ^(max) amounts at anypoint in time due to the specifications of the battery, that is,0≦q_(i)(h)≦q_(i) ^(max) for any h∈H. The initial state of charge levelq_(i)(0)≧0 is assumed to be given.

We use Ω_(G) _(i) for the set of feasibility constraints of powergeneration of device i∈N , that is, p_(i)∈Ω_(G) _(i) . Similarly, we useΩ_(s) _(i) to denote the set of feasibility constraints for the storageprofile of i∈N , s_(i):={s_(i)(h)}_(h∈H)∈Ω_(S) _(i) .

Given the constraints regarding device specifications the EDP choosesgeneration p:={p_(i)}_(i∈N) and storage s:={s_(i)}_(i∈N) profiles thatwill match supply and demand while minimizing cost,

$\begin{matrix}{\min\limits_{p,s}{\sum\limits_{i \in N}{C_{i}\left( p_{i} \right)}}} & (2) \\{{{s.t.\mspace{14mu} {\sum\limits_{i \in N}p_{i}}} - s_{i}} = d} & (3) \\{{p_{i} \in \Omega_{G_{i}}},{s_{i} \in {\Omega_{S_{i}}{\mspace{11mu} \;}{forall}\mspace{14mu} i} \in N}} & (4)\end{matrix}$

The supply demand matching constraint (3) couples the decision variablesof the devices. We denote the optimal power and storage profiles to theabove equation with p* and s*, respectively. Next, we provide a fullydecentralized algorithm based on ADMM that converges to the optimalpower generation and storage values.

The ADMM Algorithm is detailed next. For variables x∈X⊂R′, z∈Z⊂R′″, Thegeneric form of the problems that the ADMM algorithm providesdecentralized solutions to contain objective functions f(·):X→R andh(·):Z→R and linear equality constraints,

$\begin{matrix}{{\min\limits_{{x \in X},{z \in Z}}{f(x)}} + {h(z)}} & (5) \\{{{s.t.\mspace{14mu} {Ax}} + {Bz}} = c} & \;\end{matrix}$

where A∈R^(k×n), B∈R^(k×m) and c∈R^(k). Note that the objective of theabove optimization problem has the form that is separable with respectto its variables while its constraint couples the variables. The ADMMoperates on the augmented Lagrangian defined as

$\begin{matrix}{{L_{\rho}\left( {x,z,\lambda} \right)}:={{f(x)} + {h(z)} + {\lambda^{T}\left( {{Ax} + {Bz} - c} \right)} + {\frac{\rho}{2}{{{{Ax} + {Bz} - c}}}^{2}}}} & (6)\end{matrix}$

where λ∈R^(k) is the price associated with violation of the equalityconstraint and ρ>0 is a penalty parameter that penalizes infeasibilityof (5). The algorithm consists of a coordinate descent in the primalvariables in an alternating manner followed by an ascent step in theprice variable,

x _(t+1):=argmin_(x)L_(ρ)(x,z _(t),λ_(t))  (7)

z _(t+1):=argmin_(z)L_(ρ)(x _(t+1) ,z,λ _(t))  (8)

λ_(t+1):=λ_(t)+ρ(Ax _(t+1) +Bz _(t+1) −c)  (9)

The minimization of the augmented Lagrangian with respect to x atiteration t+1 requires values of other variables from iteration t,namely, primal variable z_(t) and price variable λ_(t) in (7). Theminimization of the augmented Lagrangian with respect to z at iterationt+1 requires the updated primal variable x_(t+1) and the price variableλ_(t) in (8). The order of primal updates can be interchanged, that is,we can update z first and then x; however, the second variable that isupdated still requires the updated value of the first primal variable.The dual ascent step at iteration t+1 in (9) uses the updated primalvariables x_(t+1) and z_(t+1) to ascent with step size equal to thepenalty parameter ρ.

While the form of the EDP in (2)-(4) belongs to the type of problemsthat ADMM is designed for, the ADMM algorithm presented above is not afully decentralized update. It is possible to see this from thediscussion above where each primal variable update requires previouslyupdated primal variables. This means that devices need to receive themost recent updates from all of the devices that updated before them inorder to update their primal variables. Furthermore the dual ascent step(9) requires a centralized coordinator that has access to network-wideupdated primal variables. Hence, we introduce a communication networkand present a fully decentralized solution to EDP utilizing the dualconsensus ADMM (DC-ADMM).

Consider a connected network with set of nodes corresponding to devicesin the grid N and an edge set E where pair of nodes (i,j) belong to E ifi can send information to and receive information from j, i

j, that is, E:={(i,j):i

j,i∈N,j∈N}. The neighborhood set of i is the set of agents from whichagent i can receive information from N_(i):={(j,i)∈E:j∈N}. We adopt theconvention that device i is not the neighbor of itself, that is,i∉N_(i).

We relax the coupling equality constraint (3) of the EDP problem withthe price variables λ to obtain the following Lagrangian

$\begin{matrix}{{L\left( {\left\{ p_{i} \right\}_{i \in N},\left\{ s_{i} \right\}_{i \in N},\lambda} \right)} = {\sum\limits_{i \in N}{\left( {{C_{i}\left( p_{i} \right)} + {\lambda^{T}\left( {p_{i} - s_{i}} \right)} - {\lambda^{T}d\text{/}N}} \right).}}} & (10)\end{matrix}$

The dual function for the relaxed EDP is obtained by maximizing thenegative of the above Lagrangian with respect to the primal variableswhich we can do separately for each device,

$\begin{matrix}{{g(\lambda)}:={\sum\limits_{i \in N}{\underset{s_{i} \in \Omega_{S_{i}}}{\max\limits_{p_{i} \in \Omega_{G_{i}}}}{- {\left( {{C_{i}\left( p_{i} \right)} + {\lambda^{T}\left( {p_{i} - s_{i}} \right)} - {\lambda^{T}d\text{/}N}} \right).}}}}} & (11)\end{matrix}$

We define the local dual function resulting from maximization of localvariables of i as

g_(i)(λ) := max_(p_(i) ∈ Ω_(G_(i)), s_(i) ∈ Ω_(S_(i)))−C_(i)(p_(i)) − λ^(T)(p_(i) − s_(i))

and rewrite the dual function above as a sum of local dual functions,

$\begin{matrix}{{g(\lambda)}:={{\sum\limits_{i \in N}{g_{i}(\lambda)}} + {\lambda^{T}d\text{/}{N.}}}} & (12)\end{matrix}$

The minimization of (12) with respect to λ yields the optimal pricevariables and the optimal primal variables when the original EDP problemin (2) has zero duality gap. However, λ is a global variable associatedwith the equality constraint in (2) and solution to (12) requiresinformation from all devices. In order to solve the dual problem abovein a decentralized manner we introduce the local copies of the pricevariable, that is, i's local copy of λ is λ_(i). Then we canequivalently represent the minimization of (12), min_(λ)g(λ) in terms oflocal copies of the price variable given a connected network,

$\begin{matrix}{{\min\limits_{\lambda_{1},\ldots,\lambda_{N},{\{\gamma_{ij}\}}}{\sum\limits_{i \in N}{g_{i}\left( \lambda_{i} \right)}}} - {\lambda_{i}^{T}d\text{/}N}} & (13) \\{{{s.t.\mspace{14mu} \lambda_{i}} = \gamma_{ij}},{\lambda_{j} = {{\gamma_{ij}\mspace{14mu} {forall}\mspace{14mu} j} \in N_{i}}},{i \in N}} & (14)\end{matrix}$

where γ_(ij) are the local auxiliary variables. Note that in a connectednetwork the solution of the above optimization is equivalent to solvingmin_(λ)g(λ). Further observe that the above optimization is of the formin (5) which implies we can derive an algorithm using the same argumentsas in Section 3.1. We first form the augmented Lagrangian for the aboveproblem using the dual variables u_(ij) and v_(ij) the consensusconstraints in (14) with the penalty constant ρ>0,

$\begin{matrix}{{L_{\rho}\left( {\lambda_{1},\ldots \mspace{11mu},\lambda_{N},\left\{ {\gamma_{ij},u_{ij},v_{ij}} \right\}} \right)} = {{\sum\limits_{i \in N}{g_{i}\left( \lambda_{i} \right)}} - {\lambda_{i}^{T}d\text{/}N} + {\sum\limits_{j \in N_{i}}{u_{ij}\left( {\lambda_{i} - \gamma_{ij}} \right)}} + {v_{ij}\left( {\gamma_{ij} - \lambda_{j}} \right)} + {\frac{\rho}{2}{\sum\limits_{j \in N_{i}}{{{\lambda_{i} - \gamma_{ij}}}}^{2}}} + {{{\lambda_{j} - \gamma_{ij}}}}^{2}}} & (15)\end{matrix}$

Define the set of price variables of all the agents λ:={λ_(i)}_(i∈N) andthe set of all auxiliary variables as γ={γ_(ij)}_(j∈N) _(i) _(,i∈N).When we apply the ADMM steps in (7)-(9) to the above augmentedLagrangian, we have the following steps at iteration t:

λ _(t+1)=argmin _(λ) L _(ρ)( λ, γ _(t) ,{u _(ijt) ,v _(ijt)})  (16)

γ _(t+1)=argmin _(γ) L _(ρ)( γ _(t+1), γ,{u_(ijt) ,v _(ijt)})  (17)

u _(ijt+1) =u _(ijt)+ρ(γ_(it+1)−γ_(ijt+1))  (18)

v _(ijt+1) =v _(ijt)+ρ(γ_(jt+1)−γ_(ijt+1))  (19)

Starting from the auxiliary variable updates (17) and primal variableupdates (16) and using their decomposable structure into Σ_(i)|N_(i)|and N quadratic sub-problems, respectively, the set of updates above(16)-(19) simplifies and decouples into the following updates

$\begin{matrix}{\mspace{79mu} {y_{{it} + 1} = {y_{it} + {\rho {\sum\limits_{j \in N_{i}}\lambda_{it}}} - \lambda_{jt}}}} & (20) \\{\lambda_{{it} + 1} = {{\arg \; {\min_{\lambda_{i}}{g_{i}\left( \lambda_{i} \right)}}} - {\lambda_{i}^{T}{d/N}} + {\sum\limits_{j \in N_{i}}{y_{{jt} + 1}^{T}\lambda_{i}}} + {\rho {\sum\limits_{j \in N_{i}}{{{\lambda_{i} - \frac{\lambda_{it} + \lambda_{jt}}{2}}}}^{2}}}}} & (21)\end{matrix}$

where we define y_(it):=Σ_(j∈N) _(i) u_(ijt)+v_(ijt) when initial dualvariables are all zero u_(ij0)=0 and v_(ij0)=0. The minimization in (21)is actually a min-max optimization problem that implicitly includes themaximization of the primal variables p_(i) and s_(i) in the dualfunction g_(i)(·). When C_(i)(·) is convex and strong duality holds forthe EDP (2)-(4), they provide the following closed form solution for themin-max problem in (21) using the minimax theorem

$\begin{matrix}{{\lambda_{{it} + 1} = {\frac{1}{2{N_{i}}}\left( {{\sum\limits_{j \in N_{i}}\left( {\lambda_{it} + \lambda_{jt}} \right)} + {\frac{1}{\rho}\left( {p_{{it} + 1} - s_{{it} + 1} - {\frac{1}{N}d}} \right)} - {\frac{1}{\rho}y_{{it} + 1}}} \right)}},} & (22) \\{\left( {p_{{it} + 1},s_{{it} + 1}} \right) = {{\arg \; {\min_{{p_{i} \in \Omega_{G_{i}}},{s_{i} \in \Omega_{S_{i}}}}{C_{i}\left( p_{i} \right)}}} + {\frac{\rho}{4{N_{i}}}{{{{\frac{1}{\rho}\left( {p_{i} - s_{i} - {\frac{1}{N}d}} \right)} - {\frac{1}{\rho}y_{{it} + 1}} + {\sum\limits_{j \in N_{i}}\left( {\lambda_{it} + \lambda_{jt}} \right)}}}_{2}^{2}.}}}} & (23)\end{matrix}$

Observe that the price variable update in (22) requires the updatedprimal variables of time t+1 from (23). Hence device i first updates theprimal variables and then the price variable. The updates for device iare summarized in Algorithm 1.

Algorithm 1 d-EDP updates at device i Require: Initialize primalvariables p_(i0), s_(i0), λ_(i0) and dual variables y_(i0) = 0. Set t =0. Require: Determine stopping condition, e.g., maximum number of stepsT ∈ 

 |⁺. while Stopping Condition Not Reached do [1] Transmit λ_(it) andreceive λ_(jt) from j ∈ 

 . [2] Compute y_(it+1) using ( 

 ) [3] Update primal variables p_(it+1), s_(it+1) using ( 

 ). [4] Compute prices λ_(it+1) using ( 

 ). [5] Set t= t+1. end while

Algorithm 1 solves the dual EDP in a fully decentralized manner. Theinitialization consists of setting dual variables y_(i0) to zero. Othervariables p_(i0), s_(i0), λ_(i0) can be arbitrarily set. The algorithmat time t starts by sending local price variables λ_(it) and observingneighbors' local price variables λ_(N) _(i) _(t):={λ_(jt):j∈N_(i)}. Thealgorithm is synchronous in that device i requires prices of all of itsneighbors from iteration t. Then in step 2 device i averages theneighbors' price variables to update its dual variable (20). Along withobserved price variables λ_(N) _(i) _(t), the dual variables y_(it+1)are used to update the primal power and storage variables following (23)in step 3. Finally in step 4 device i updates its local price variablek_(it+i) using all of the observed and updated variables according to(22). The algorithm continues by moving the iteration step forward.

The derivation above is worth retracing. The primal EDP problem in(2)-(4) contains a power balance constraint that couples the variablesof all the devices. Therefore, we consider a decentralized solutionoperating on the relaxation of the power balancing constraint. Therelaxed problem in (??), i.e., the dual EDP entails a global pricevariable λ that is associated with the price of power imbalance. We thenwrite an equivalent representation of the dual EDP as a dual consensusEDP in (13)-(14) where each device carries their local copy of theprice. Applying the ADMM algorithm to the dual consensus EDP yields afully decentralized solution.

The iterations of Algorithm 1 asymptotically converges to optimalvariables when the problem is convex, the network (N,E) is connected andstrong duality holds. We assume that the cost C_(i)(p_(i)) is convex inp_(i)∈Ω_(G) _(i) and the network is connected for the centralized EDP in(2)-(4). A sufficient condition for strong duality is Slater's conditionwhich requires that there exists a strictly feasible point. For a set oflinear equality and inequality, this condition relaxes to the existenceof a feasible point. For the EDP problem in (2)-(4) the constraints areall affine. Furthermore, we assume that the energy system is connectedto the grid which can satisfy demand at all times. This assumption makessure that there exists a feasible point {p_(i),s_(i)}_(i∈N) thatsatisfies power balance constraint (3) and other device specificconstraints (4). Consequently, the assumptions of Theorem 2 in [13] areall met and the iterations of Algorithm 1 converge to the optimal, thatis, p_(it)→p*_(i), s_(it)→s*_(i). The d-EDP is such that the solutionyields optimal local prices along with the optimal power and storageprofiles, that is, λ_(it)→λ*. The local optimal prices can then be usedto design smart pricing policies such as real time pricing for demandresponse management.

Given a time horizon H a centralized receding horizon control for EDPsolves the optimization in (2) for the whole horizon to obtain power andstorage profiles but only uses the first element of the optimal profilefor step h=0. Before h=1, the EDP is solved for hours h=1 to H+1 and thescheduled element for h=1 is applied and the horizon is propagated byone again. In order to implement the decentralized receding horizoncontrol, we use the d-EDP algorithm for each hour and furthermore werequire a communication protocol that synchronizes devices for startingthe updates for the next time step. Note that the updates in d-EDPrequire only local forecasts and device specifications. Hence eachdevice can update its forecasts locally. We assume the demand profile isforecasted by a load device and is communicated to all the devices.

The proposed communication protocol for device i is detailed inAlgorithm 2. Each device starts the algorithm by updating its localforecasts for the operating horizon. Then each device sends a request tostart planning for the horizon in step 2 and waits to receive requestsfrom all their neighbors in step 3. When all neighboring devices sendtheir requests, device i starts the d-EDP Algorithm 1 in step 4. OnceAlgorithm 1 is complete, device I applies the first element of thescheduled power and storage profile in step 5. When the power isdispatched, the device propagates its time in step 6 and goes back tostep 1 to start planning for the the current time horizon.

Algorithm 2 Decentralized receding horizon at device i Require:Initialize time h = 0. Require: Initial demand forecast profile d andlocal forecasts if applicable. loop [1] Update local forecasts for h toH + h. [2] Request neighbors to start planning. [3] Wait until allneighbors also send their requests. [4] Do d-EDP (Algorithm 

 ). [5] Apply the first element of p_(iT)*(h) and s_(iT)*(h). [6]Advance time h = h + 1. end loop

Changes to the network can occur when a device leaves or a new devicejoins. When a device is removed all the devices interrupt theiroperations and update their network information, that is, theirneighborhood list N_(i) and the total number of devices N. Then theyrestart Algorithm 2 from step 1. When a device is added, devices updatetheir network information at the beginning of the next time step, thatis, after advancing time in step 6. This means that the new device isadmitted to the system in the next time step. The new device updates itsnetwork information upon connection to the network and starts from step1 and waits at step 3 for his neighbors to send requests. For acentralized solution to the EDP a device removal or addition impliesreconfiguring the optimization problem by removing or adding newvariables, constraints and cost functions. Reformulating theoptimization problem can be cumbersome when the network is changingfrequently. The steps of the decentralized receding horizon methoddescribed in Algorithm 2 require that the devices only need theirneighbor list and the total number of devices in the system.

In one embodiment, a Decentralized Management Platform includes amulti-agent framework and a decentralized control method to manage thelarge-scale community-level energy systems. The Multi-agent frameworkfor energy systems includes a procedural architecture to add devices asagents into the energy system framework and submit the services theyprovide for or request from other agents. This framework is dynamic inwhich agents can join or leave the energy system at any time withoutinterrupting the rest of the system. Supplier agent includes deviceswhich can provide power to supply the load submit their service as asupplier and play as an active agent in the multi-agent framework. Theexample of these agents can be grid, diesel, PV, battery, etc. It shouldbe noted that battery can be both supplier agent and demand agent.Demand agents includes loads in the network will submit their service asdemand in multi-agent framework and inform supplier agents about theirrequested load value.

The system provides a reliable and scalable decentralized platform thatefficiently manages the operation of a large-scale energy system basedon requested load, available renewable generation, time-of-use gridelectricity rate, battery condition, diesel generator loading-basedcost, etc. In this dynamic platform, any device can join or leave theenergy system at any time without interrupting the rest of the system.

The system may be implemented in hardware, firmware or software, or acombination of the three. FIG. 2 shows an exemplary computer to executeobject detection. In the decentralized approach of the present system,each device will have its own programmable computer (processor, embeddedsystem) that communicates with other devices' computers (processors,embedded systems), and they collectively solve the energy managementproblem.

By way of example, a block diagram of a computer to support the systemis discussed next. The computer preferably includes a processor, randomaccess memory (RAM), a program memory (preferably a writable read-onlymemory (ROM) such as a flash ROM) and an inputoutput (IO) controllercoupled by a CPU bus. The computer may optionally include a hard drivecontroller which is coupled to a hard disk and CPU bus. Hard disk may beused for storing application programs, such as the present invention,and data. Alternatively, application programs may be stored in RAM orROM. IO controller is coupled by means of an IO bus to an IO interface.IO interface receives and transmits data in analog or digital form overcommunication links such as a serial link, local area network, wirelesslink, and parallel link. Optionally, a display, a keyboard and apointing device (mouse) may also be connected to IO bus. Alternatively,separate connections (separate buses) may be used for IO interface,display, keyboard and pointing device. Programmable processing systemmay be preprogrammed or it may be programmed (and reprogrammed) bydownloading a program from another source (e.g., a floppy disk, CD-ROM,or another computer).

Each computer program is tangibly stored in a machine-readable storagemedia or device (e.g., program memory or magnetic disk) readable by ageneral or special purpose programmable computer, for configuring andcontrolling operation of a computer when the storage media or device isread by the computer to perform the procedures described herein. Theinventive system may also be considered to be embodied in acomputer-readable storage medium, configured with a computer program,where the storage medium so configured causes a computer to operate in aspecific and predefined manner to perform the functions describedherein.

The invention has been described herein in considerable detail in orderto comply with the patent Statutes and to provide those skilled in theart with the information needed to apply the novel principles and toconstruct and use such specialized components as are required. However,it is to be understood that the invention can be carried out byspecifically different equipment and devices, and that variousmodifications, both as to the equipment details and operatingprocedures, can be accomplished without departing from the scope of theinvention itself.

What is claimed is:
 1. A method for power management, comprising:applying a decentralized control to manage a large-scale community-levelenergy system; obtaining a global optimal solution satisfyingconstraints between the agents representing the energy system's devicesas a state-based potential game with a multi-agent framework;independently optimizing each agent's output power while consideringoperational constraints and assuring a pure Nash equilibrium (NE),wherein a state space helps coordinating the agents' behavior in energysystem to deal with system-wide constraints including supply demandbalance, battery charging power constraint and satisfy system-wide anddevice-level (local) operational constraints; and controllingdistributed generations (DGs) and storage devices using the agent'soutput.
 2. The method of claim 1, comprising adding devices as agentsinto the energy system framework and submitting the agent's services orrequest from other agents, wherein agents dynamically join or leave theenergy system at any time without interrupting the rest of the system.3. The method of claim 1, comprising handling supplier agents or devicesto provide power to supply the load and submit their service as asupplier.
 4. The method of claim 3, comprising playing as an activeagent in the multi-agent framework, wherein the agents include grid,diesel, PV, or battery.
 5. The method of claim 1, comprising handling ademand agent, wherein each load in the network submit its service asdemand in the multi-agent framework and inform supplier agents about itsrequested load value.
 6. The method of claim 1, comprising applying adistributed dispatching strategy for energy sources and loads tominimize a total marginal cost of operation for the energy system andsatisfy device-level and system-wide level operational constraints. 7.The method of claim 6, wherein the dispatching strategy comprisesapplying a game theory, a state-based potential game, a learningalgorithm, a gradient play or a Newton method.
 8. The method of claim 1,comprising determining a total cost of operation for the energy system(system-wide cost model) as a summation of the devices' operational cost(local cost models).
 9. The method of claim 1, wherein system-wideoperational constraints are satisfied through passing message packagesand negotiations between the agents and agent local constraints arehandled locally by a related agent.
 10. The method of claim 1, whereinthe agents use one or more learning algorithms at each iteration of thegame.
 11. A method for power management, comprising: applying adecentralized management platform based on multiagent framework andstate-based potential game; analytically obtaining a global optimalsolution satisfying constraints between agents (energy system'sdevices); applying the power management as a game where each agent isable to independently optimize its output power while considering itsoperational constraints; assuring a Nash equilibrium (NE) exists. 12.The method of claim 11, comprising using a state-based potential gamewhere a state space added to the game helps with coordinating theagents' behavior in energy system to deal with system-wide constraintsincluding supply demand balance, battery charging power constraint,wherein the NE of the game is efficient with respect to system totalcost of operation and satisfies system-wide and device-level (local)operational constraints.